JP2018146491A - Analysis method of composite material and computer program for analyzing composite material - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an analysis method of a composite material which can perform a numerical analysis of the composite material while holding a filler aggregation structure, and a computer program for analyzing the composite material.SOLUTION: An analysis method of a composite material is an analysis method of a composite material using an analysis model for a composite material by a molecular dynamics method by use of a computer. The method comprises: a first step ST11 of creating an analysis model for a composite material including a polymer model modeling a polymer and a plurality of filler models modeling fillers; a second step ST12 of creating at least one aggregation structure holding bond between the filler models; and a third step ST13 of performing a numerical analysis of the analysis model for a composite material in which the aggregation structure holding bond is created.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a composite material analysis method and a composite material analysis computer program. For example, the present invention relates to a composite material analysis method and a composite material analysis computer program capable of analyzing a composite material including a filler and a polymer.

  Conventionally, a simulation method of a composite material using molecular dynamics has been proposed (see, for example, Patent Document 1). In the composite material simulation method described in Patent Document 1, a composite material model including a polymer model and a filler model is created in a model creation region, and then the polymer model is coupled to a coupling position on the filler model surface. Thus, in the method for creating the composite material analysis model described in Patent Document 1, it is possible to analyze the influence of the bonding state of the polymer particles on the filler surface on the material properties of the composite material.

Japanese Patent Laying-Open No. 2015-064242

  By the way, in order to accelerate the development of a fuel-efficient tire, it is effective to clarify the relationship between energy loss (hysteresis) accompanying tire deformation and the tire nanostructure. It is considered that the material characteristics of the composite material used for the fuel-efficient tire are strongly influenced by the arrangement and structure of the filler. For this reason, in the material development of the composite material, it is effective to investigate, for example, the influence of the filler aggregation structure existing in the composite material on the mechanical response of the composite material.

  However, in the conventional analysis method for composite materials, the filler model has a substantially spherical shape. Therefore, under general analysis conditions, there are few regions where the attractive force acts between the filler models. It was difficult to maintain the filler aggregation structure in the material model. It is also conceivable to set an interaction potential with a large effective range of attractive force acting between the filler models during numerical analysis to maintain the filler aggregation structure. In this case, the calculation time of numerical analysis increases enormously. There is. For this reason, in the conventional composite material analysis method, various numerical analyzes are not sufficiently performed in a state where the filler aggregate structure in the composite material model is maintained.

  The present invention has been made in view of such circumstances, and a composite material analysis method and a composite material analysis computer program capable of performing various numerical analyzes in a state in which a filler aggregation structure in a composite material model is maintained. The purpose is to provide.

  The composite material analysis method of the present invention is a composite material analysis method using a composite material analysis model created by a molecular dynamics method using a computer, and is a polymer model obtained by modeling a polymer and a filler model. A first step of creating a model for analyzing the composite material including a plurality of filler models, a second step of creating at least one aggregated structure holding bond between the plurality of filler models, and the aggregated structure holding bond And a third step of performing a numerical analysis of the composite material analysis model created.

  According to the composite material analysis method of the present invention, at least one aggregate structure retention bond is provided between a plurality of filler models of a composite material analysis model, and two or more of the composite material analysis models at the time of numerical analysis can be obtained. Since the agglomeration of the filler model can be maintained, various numerical analyzes can be performed while the filler agglomeration structure is maintained. In addition, by creating an aggregated structure-retaining bond, it is possible to maintain the filler aggregated structure without setting an interaction potential with a large effective range between filler models during numerical analysis, which can greatly reduce calculation time. Become. Therefore, the composite material analysis method enables numerical analysis of the composite material in a state in which the filler aggregation structure in the composite material is maintained.

  In the composite material analysis method of the present invention, it is preferable to further include a step of crosslinking the polymer model. With this method, the composite material analysis method creates a cohesive retention bond between the filler models in a state in which the polymer model is previously cross-linked through a cross-linking reaction, so various numerical analyzes of the composite material in consideration of cross-linking of the polymer model Is possible. Therefore, the composite material analysis method enables more accurate numerical analysis of the composite material in a state where the filler aggregation structure in the composite material is maintained.

  In the composite material analysis method of the present invention, it is preferable that the aggregated structure-retaining bond is a bond whose extension length of the bond length is not defined. According to this method, the analysis method of the composite material does not break the aggregate structure holding bond even when the distance between the pair of filler models provided with the aggregate structure holding bond is increased during the numerical analysis. This enables the composite material analysis method to more reliably retain the filler aggregation structure in the composite material analysis model, thus avoiding the failure of numerical analysis due to the elimination of the filler aggregation structure during numerical analysis. It becomes possible to do.

  In the composite material analysis method of the present invention, it is preferable that the aggregated structure-retaining bond is created between central portions of the filler model. By this method, the analysis method of the composite material can be used between a pair of filler models in which an agglomerated structure-retaining bond is created even when a filler model in which a plurality of filler particles are gathered into a substantially spherical shape rotates during numerical analysis. A change in distance can be reduced. As a result, the analysis method of the composite material enables more accurate numerical analysis of the composite material while maintaining the filler aggregation structure in the composite material.

  In the composite material analysis method of the present invention, it is preferable that an equilibrium length of the aggregated structure-retaining bond is equal to or greater than a sum of radii of a pair of filler models provided with the aggregated structure-retaining bond. By this method, the analysis method of the composite material can prevent a collision due to the approach between a pair of filler models provided with an agglomeration structure holding bond at the time of numerical analysis, so it is possible to avoid an increase in stress in numerical analysis. Become. As a result, the analysis method of the composite material enables more accurate numerical analysis of the composite material while maintaining the filler aggregation structure in the composite material.

  In the composite material analysis method of the present invention, it is preferable to subtract the stress based on the aggregated structure holding bond from the stress strain curve obtained as a calculation result by the numerical analysis. By this method, the analysis method of the composite material can remove the energy necessary for holding the filler aggregate structure by the aggregate structure retention bond during the numerical analysis from the stress strain curve obtained by the numerical analysis. It is possible to accurately evaluate the effect of the polymer chain on the polymer chain.

  The computer program for analyzing a composite material according to the present invention causes a computer to execute the above-described composite material analysis method.

  According to the computer program for analyzing a composite material of the present invention, it is only necessary to provide at least one aggregated structure holding bond between a plurality of filler models of the composite material analysis model. Since aggregation of two or more filler models can be maintained, various numerical analyzes can be performed while maintaining the filler aggregation structure. In addition, by creating an aggregated structure-retaining bond, it is possible to maintain the filler aggregated structure without setting an interaction potential with a large effective range between filler models during numerical analysis, which can greatly reduce calculation time. Become. Therefore, the composite material analysis method enables numerical analysis of the composite material in a state in which the filler aggregation structure in the composite material is maintained.

  ADVANTAGE OF THE INVENTION According to this invention, the analysis method of the composite material which can perform the numerical analysis of a composite material in the state holding the filler aggregation structure, and the computer program for analysis of a composite material are realizable.

FIG. 1 is a flowchart showing an outline of a composite material analysis method according to the first embodiment of the present invention. FIG. 2 is a conceptual diagram illustrating an example of an analysis model created by the composite material analysis model creation method according to the first embodiment. FIG. 3 is an explanatory diagram showing an example of a method for creating a composite material analysis model according to the first embodiment. FIG. 4 is an explanatory diagram illustrating an example of a method for creating a composite material analysis model according to the first embodiment. FIG. 5 is an explanatory diagram showing an example of a method for creating a composite material analysis model according to the first embodiment. FIG. 6 is an explanatory diagram showing an example of a method for creating a composite material analysis model according to the first embodiment. FIG. 7A is an explanatory diagram showing an example of a method for creating a composite material analysis model according to the first embodiment. FIG. 7B is an explanatory diagram illustrating an example of a method for creating a composite material analysis model according to the first embodiment. FIG. 7C is an explanatory diagram illustrating an example of a method for creating a composite material analysis model according to the first embodiment. FIG. 8 is a flowchart showing an outline of a method of creating a composite material analysis model according to the second embodiment of the present invention. FIG. 9A is an explanatory diagram illustrating an example of a method for creating a composite material analysis model according to the second embodiment. FIG. 9B is an explanatory diagram illustrating an example of a method for creating a composite material analysis model according to the second embodiment. FIG. 10 is a functional block diagram of an analysis apparatus that executes a composite material analysis method and a composite material analysis method according to an embodiment of the present invention. FIG. 11 is a conceptual diagram of a composite material analysis model according to examples and comparative examples of the present invention. FIG. 12A is a conceptual diagram of an analysis model of a composite material after elongation analysis according to Example 1 of the present invention. FIG. 12B is a conceptual diagram of a composite analysis model after elongation analysis according to Comparative Example 1 of the present invention. FIG. 12C is a conceptual diagram of a composite analysis model after elongation analysis according to Comparative Example 2 of the present invention. FIG. 13 is a diagram showing a stress strain curve of an analysis model of a composite material according to an example of the present invention.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. In addition, this invention is not limited to each following embodiment, It can implement by changing suitably.

(First embodiment)
FIG. 1 is a flowchart showing an outline of the composite method according to the first embodiment of the present invention. As shown in FIG. 1, the composite material analysis method according to this embodiment is a composite material analysis method using a composite material analysis model created by a molecular dynamics method using a computer. This composite material analysis method includes a first step ST11 of creating a composite material analysis model including a polymer model modeling a polymer and a plurality of filler models modeling a filler, and at least one between the plurality of filler models. It includes a second step ST12 for creating one aggregated structure-retaining bond, and a third step ST13 for executing a numerical analysis of the composite material analysis model in which the aggregated structure-retaining bond is created.

  FIG. 2 is a conceptual diagram showing an example of the composite material analysis model 1 according to the present embodiment. As shown in FIG. 2, the composite material analysis model 1 according to the present embodiment is modeled, for example, in a model creation region A that is a substantially cubic virtual space whose one side is a distance L in length. . The model creation area A is a three-dimensional space that extends in the X-axis, Y-axis, and Z-axis directions orthogonal to each other. The composite material analysis model 1 includes a plurality of filler models 11A, 11B, 11C, and 11D obtained by modeling a plurality of filler particles 11a, and a plurality of models obtained by modeling a plurality of polymer particles 21a and bonding chains 21b. Polymer model 21. In this composite material analysis model 1, a plurality of filler models 11A, 11B, 11C, and 11D are distributed in the model creation region A. The plurality of polymer models 21 are distributed and arranged between the plurality of filler models 11A, 11B, 11C, 11D.

  In the example illustrated in FIG. 2, an example in which the composite material analysis model 1 includes four filler models 11 is described. However, the number of filler models to be modeled is not limited. The composite material analysis model 1 may include three or more filler models 11. In FIG. 2, only four polymer models 21 are shown, but in the composite material analysis model 1, a plurality of polymer models 21 exist throughout the model creation region A. Furthermore, in the example illustrated in FIG. 2, the model creation region A is illustrated as an example of a substantially rectangular parallelepiped virtual space, but may be any shape such as a spherical shape, an elliptical shape, a rectangular parallelepiped shape, or a polyhedral shape.

  Examples of the filler include carbon black, silica, and alumina. The filler particles 11a are modeled by collecting a plurality of filler atoms. The filler particles 11a constitute a filler particle group by aggregating a plurality of filler particles 11a. The relative position of the filler particles 11a is specified by a bond chain (not shown) between the plurality of filler particles 11a. This bond chain (not shown) functions as a spring in which an equilibrium length, which is a bond distance between filler particles 11a, and a spring constant are defined, and binds between the filler particles 11a. The bond chain is a bond in which the relative position of the filler particle 11a and the potential at which force is generated by twisting, bending, or the like are defined. The filler models 11A, 11B, 11C, and 11D are numerical data (including the mass, volume, diameter, and initial coordinates of the filler particles 11a) for handling the filler with molecular dynamics. Numerical data of the filler model 11 is input to the computer.

  Examples of the polymer include rubber, resin, and elastomer. The polymer particle 21a is modeled by collecting a plurality of polymer atoms. The polymer particles 21a constitute a polymer particle group by aggregating a plurality of polymer particles 21a. A modifier is added to the polymer as needed to enhance the affinity with the filler. Examples of the modifier include a hydroxyl group, a carbonyl group, and a functional group of an atomic group. The polymer model 21 is modeled by filling a plurality of polymer atoms and polymer particles 21a, which are aggregates of a plurality of polymer atoms, into the model creation region A at a predetermined density. The polymer particle 21a is bound by a binding chain 21b between the plurality of polymer particles 21a, and the relative position is specified. The binding chain 21b functions as a spring in which an equilibrium length, which is a binding distance between the polymer particles 21a, and a spring constant are defined, and restrains the polymer particles 21a. The bond chain 21b is a bond in which the relative position of the polymer particle 21a and the potential at which force is generated by twisting, bending, or the like are defined. The bonding chain 21b is also bonded as a cross-linking bond (not shown) between the polymer models 21 in which a plurality of polymer particles are connected in series. The polymer model 21 is numerical data (including the mass, volume, diameter, initial coordinates, and the like of the polymer particle 21a) for handling the polymer by molecular dynamics. Numerical data of the polymer model 21 is input to a computer.

  Note that in this embodiment, an example in which a composite material to be analyzed contains a filler and a polymer that is a polymer material will be described; however, the present invention is also applicable to a composite material containing two or more kinds of substances. Is possible. The present invention is also applicable to composite materials containing objects other than fillers and polymers.

  Next, a composite material analysis method according to the present embodiment will be described in detail with reference to FIGS. 3 to 7C are explanatory diagrams illustrating an example of a composite material analysis method according to the present embodiment. 3C, the plan view of FIG. 2 is schematically shown, and the polymer model 21 is omitted.

  In the first step ST11, as shown in FIG. 2, in the model creation region A, a filler model 11 and a plurality of polymer particles 21a, which are modeled by aggregating a plurality of filler particles 11a, are connected via a bonding chain 21b. A composite analysis model 1 including a polymer model 21 connected and modeled is created. In the first step ST11, as shown in FIG. 3, the four filler models 11A, 11B, 11C, and 11D are modeled in a state where a plurality of filler particles 11a are gathered in a substantially circular shape in plan view. Further, the four filler models 11A, 11B, 11C, and 11D are modeled in an aggregated state in which they are aggregated at a predetermined distance from each other.

  Next, in the second step ST12, as shown in FIG. 4, aggregated structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD are created between the four filler models 11A, 11B, 11C, and 11D, respectively. The aggregated structure-retaining bond 12AB includes filler particles 11a existing on the surface of the filler model 11A and filler particles 11a existing on the surface of the filler model 11B so that the distance between the filler model 11A and the filler model 11B is the shortest. Created during. Aggregate structure retention bond 12AC includes filler particles 11a present on the surface of filler model 11A and filler particles 11a present on the surface of filler model 11C so that the distance between filler model 11A and filler model 11C is the shortest. Created during. Aggregate structure retention bond 12AD includes filler particles 11a present on the surface of filler model 11A and filler particles 11a present on the surface of filler model 11D so that the distance between filler model 11A and filler model 11D is the shortest. Created during. Aggregate structure retention bond 12BC includes filler particles 11a existing on the surface of filler model 11B and filler particles 11a existing on the surface of filler model 11C so that the distance between filler model 11B and filler model 11C is the shortest. Created during. Aggregate structure retention bond 12BD includes filler particles 11a existing on the surface of filler model 11B and filler particles 11a existing on the surface of filler model 11D so that the distance between filler model 11B and filler model 11D is the shortest. Created during. The aggregated structure-retaining bond 12CD includes filler particles 11a present on the surface of the filler model 11C and filler particles 11a present on the surface of the filler model 11D so that the distance between the filler model 11C and the filler model 11D is the shortest. Created during.

  The aggregated structure-retaining bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD are virtual springs in which a predetermined equilibrium length and a spring constant are defined for maintaining the aggregated state between the filler models 11A, 11B, 11C, and 11D. And functions between the filler models 11A, 11B, 11C, and 11D. Further, the aggregated structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD are provided between the filler models 11A, 11B, 11C, and 11D in order to maintain the aggregated state between the filler models 11A, 11B, 11C, and 11D. Those having a stronger binding force than intermolecular force and weaker than hydrogen bond are preferred. By providing such aggregated structure-retaining bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD, the aggregated state between the filler models 11A, 11B, 11C, and 11D is compared with the case where the aggregated state is held only by attractive force. Can be held easily and the calculation time can be greatly reduced.

  In the example shown in FIG. 4, the aggregated structure holding bonds 12AB, 12AC, 12AD, 12BC, and 12BD are provided between the filler particles 11a that are arranged at positions where the distance between the filler models 11A, 11B, 11C, and 11D is the shortest. However, the filler particles 11a provided with the aggregated structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD can be appropriately changed.

  As shown in FIG. 5, the aggregated structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD may be created between the center portions PA, PB, PC, and PD of the filler models 11A, 11B, 11C, and 11D. Good. In the example shown in FIG. 5, the aggregated structure-retaining bond 12AB is created between the filler particles 11a present at the center portion PA of the filler model 11A and the filler particles 11a present at the center portion PB of the filler model 11B. Agglomerated structure-retaining bond 12AC is created between filler particles 11a present at center PA of filler model 11A and filler particles 11a present at center PC of filler model 11C. Agglomerated structure-retaining bond 12AD is created between filler particles 11a present at center PA of filler model 11A and filler particles 11a present at center PD of filler model 11D. The aggregated structure-retaining bond 12BC is created between the filler particles 11a present at the center portion PB of the filler model 11B and the filler particles 11a present at the center portion PC of the filler model 11C. Agglomerated structure-retaining bond 12BD is created between filler particles 11a present at center portion PB of filler model 11B and filler particles 11a present at center portion PD of filler model 11D. The aggregated structure-retaining bond 12CD is created between the filler particles 11a present at the central portion PC of the filler model 11C and the filler particles 11a present at the central portion PD of the filler model 11D.

  As described above, the aggregated structure-retaining bonds 12AB, 12BC, 12CD, and 12AD are created between the central portions PA, PB, PC, and PD of the filler models 11A, 11B, 11C, and 11D to thereby analyze the composite material model 1. Even when the filler models 11A, 11B, 11C, and 11D in which a plurality of filler particles 11a are gathered into a substantially spherical shape rotate in the numerical analysis, the aggregated structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD It is possible to reduce the change in the distance between the pair of filler models 11A, 11B, 11C, and 11D for which the As a result, a more accurate numerical analysis of the composite material can be performed while maintaining the filler aggregation structure.

  In the example shown in FIGS. 4 and 5, an example in which six aggregated structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD are created between four filler models 11A, 11B, 11C, and 11D will be described. However, the number of aggregated structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD, 12CD and filler models 11A, 11B, 11C, 11D can be changed as appropriate. For example, in the case of performing a numerical analysis that holds the filler aggregate structure of the two filler models 11A and 11B, the aggregate structure holding bond 12AB may be provided. Moreover, when performing the numerical analysis which hold | maintained the filler aggregation structure of three filler models 11A, 11B, and 11C, what is necessary is just to set at least 2 of aggregation structure holding | maintenance coupling | bonding 12AB, 12BC, and 12AC. Moreover, when performing the numerical analysis which hold | maintains the filler aggregation structure of four filler models 11A, 11B, 11C, and 11D, what is necessary is just to set at least 3 of aggregation structure holding | maintenance coupling | bonding 12AB, 12AC, and 12AD, for example.

  Further, as shown in FIG. 6, when the aggregated structure holding bond 12AB is provided between the center portions PA and PB of the pair of filler models 11A and 11B, the potential of the aggregated structure holding bond 12AB between the filler models 11A and 11B The equilibrium length dAB is preferably equal to or greater than the sum of the radius dA of the pair of filler models 11A and the radius dB of the filler models 11B provided with the aggregated structure holding bond 12AB. Thus, even when the pair of filler models 11A and 11B approach each other at the time of numerical analysis of the analysis model 1 for the composite material, the filler models 11A and 11B are formed by the aggregated structure holding bond 12AB that functions as a virtual spring. Is pushed back, so that the collision between the filler models 11A and 11B can be prevented. As a result, it is possible to avoid an increase in the stress of the numerical analysis due to the collision of the filler models 11A and 11B. Therefore, it is possible to perform a more accurate numerical analysis of the composite material while maintaining the filler aggregation structure. Further, the equilibrium equilibrium length dAB of the aggregate structure holding bond 12AB is more preferably the sum of the radius dA of the pair of filler models 11A provided with the aggregate structure holding bond 12AB and the radius dB of the filler model 11B. Thereby, in addition to the effect mentioned above, filler model 11A, 11B can be aggregated by a higher density.

  In addition, the aggregated structure-retaining bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD shown in FIG. 4 are preferably those in which the bond length is not defined. As shown in FIGS. 7A to 7C, during the numerical analysis of the composite material analysis model 1, the filler models 11A, 11B, 11C, and 11D of the composite material analysis model 1 before the numerical analysis shown in FIG. The distance between the filler models 11A, 11B, 11C, and 11D increases and the aggregated structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD extend significantly from the time of creation. The filler aggregate structure may be eliminated by cutting. In such a case, the aggregate structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD are defined by defining a potential in which the extended length of the equilibrium length is not defined in the aggregate structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD, 12CD. , 12CD can be prevented, and the filler aggregate structure can be retained in the analysis model 1 of the composite material. 7B, when the filler models 11A, 11B, 11C, and 11D move toward the inside of the model creation region A, as shown in FIG. , 12AC, 12AD, 12BC, 12BD, and 12CD are contracted, so that the movement of the filler models 11A, 11B, 11C, and 11D is not hindered by the aggregated structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD.

  As described above, the aggregated structure-retaining bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD are not extended in the bond length, so that the aggregated structure-retaining bond 12AB, Even when the distance between the filler models 11A, 11B, 11C, and 11D provided with 12AC, 12AD, 12BC, 12BD, and 12CD is significantly changed, the aggregated structure holding bonds 12AB, 12AC, 12AD, 12BC, and 12BD are used. , 12CD can be retained in the composite analysis model without cutting the CD. Thereby, the analysis method of the composite material can avoid the failure of the numerical analysis due to the change in the arrangement of the filler model at the time of the numerical analysis.

  In the third step ST13, an interaction is set between the filler models 11A, 11B, 11C, and 11D and the polymer model 21, and numerical analysis is executed. By performing the numerical analysis by setting the interaction as described above, attractive force and repulsive force act between the filler models 11A, 11B, 11C, 11D and the polymer model 21, and the aggregated structure holding bonds 12AB, 12AC, 12AD. , 12BC, 12BD, and 12CD, various calculation results are obtained while the filler models 11A, 11B, 11C, and 11D each move in the model creation region A while maintaining the filler aggregation structure.

  The interaction between the filler models 11A, 11B, 11C, and 11D and the polymer model 21 is set between filler particles, between polymer particles, and between filler particles and polymer particles. The interaction between the filler models 11A, 11B, 11C, and 11D and the polymer model 21 is not necessarily set for all the filler particles 11a and the polymer particles 21a. Examples of the interaction between the filler model 11 and the polymer model 21 include chemical interaction such as attractive force and repulsive force such as intermolecular force and hydrogen bond, and physical interaction such as covalent bond. . Further, when the polymer model 21 is composed of a plurality of types of polymer particles 21a, an interaction may be set for each of the plurality of types of polymer particles 21a. Further, the interaction between the polymer particles 21a of a plurality of types and the filler model 11 may be the same or different. For example, an interaction different from the interaction between the polymer particle A and the filler particle 11a and the interaction between the polymer particle B and the filler particle 11a may be set.

  Examples of the numerical analysis include various numerical analyzes such as deformation analysis such as temperature change analysis, transformation analysis, extension analysis and shear analysis, and relaxation analysis. The calculation result obtained by these numerical analyzes may use a value such as displacement obtained as a result of the numerical analysis, or may be a distortion obtained by executing a predetermined calculation process. Among these, as the numerical analysis, deformation analysis is preferable from the viewpoint of being able to analyze the mechanical characteristics of the compound of the composite material.

  As described above, according to the present embodiment, at least one aggregate structure holding bond 12AB, 12AC, 12AD, 12BC, between the plurality of filler models 11A, 11B, 11C, 11D of the composite material analysis model 1 is used. By simply providing 12BD and 12CD, the aggregation of two or more filler models 11A, 11B, 11C, and 11D in the composite material analysis model 1 can be maintained at the time of numerical analysis, so that the filler aggregation structure is maintained. Various numerical analyzes can be performed. Also, by creating an aggregated structure-retaining bond, the filler aggregated structure can be maintained without setting an interaction potential with a large effective range between the filler models 11A, 11B, 11C, and 11D during numerical analysis, greatly increasing the calculation time. Can be reduced. Therefore, the composite material analysis method enables the numerical analysis of the composite material while maintaining the filler aggregation structure.

  In the above-described embodiment, the example in which the aggregate structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD are created in the second step ST12 has been described. However, the aggregate structure holding bonds 12AB, 12AC, 12AD, 12BC, 12BD and 12CD may be created after setting the interaction between the filler models 11A, 11B, 11C, and 11D and the polymer model 21 in the third step ST13.

(Second Embodiment)
Next, a second embodiment of the present invention will be described. In the following description, differences from the above-described first embodiment will be mainly described. In addition, the same reference numerals are given to components common to the above-described first embodiment, and description thereof is omitted.

  FIG. 8 is a flowchart showing an outline of a method of creating a composite material analysis model according to the second embodiment of the present invention. As shown in FIG. 8, the method for creating a composite material analysis model according to the present embodiment is a composite material analysis method using a composite material analysis model created by a molecular dynamics method using a computer. is there. This composite material analysis method includes a first step ST21 for creating a composite material analysis model including a polymer model modeling a polymer and a plurality of filler models modeling a filler, and at least one between the plurality of filler models. A second step ST22 for creating one aggregated structure-retaining bond, a third step ST23 for crosslinking the polymer model, and a fourth step ST24 for performing a numerical analysis of the analytical model for the composite material in which the aggregated structure-retaining bond is created including.

  Next, with reference to FIG. 9A and FIG. 9B, a method for creating a composite material analysis model according to the present embodiment will be described in detail. 9A and 9B are explanatory diagrams illustrating an example of a method for creating a composite material analysis model according to the present embodiment. In addition, in FIG. 9A and FIG. 9B, the top view of the filler model 11 shown in FIG. 2 is shown typically.

  In the first step ST21, the composite material analysis model 1 including the filler model 11 and the polymer model 21 is created as in the first embodiment described above.

  Next, in the second step ST22, the aggregated structure-retaining bond 12AB is formed between the filler models 11A, 11B, 11C, and 11D in the composite material model 10 in a state in which the crosslinked bond 21c is formed, as in the first embodiment described above. , 12AC, 12AD, 12BC, 12BD, 12CD. In the second step ST22, at least one aggregated structure holding bond 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD may be provided as in the first embodiment described above.

  Next, in the third step ST23, as shown in FIGS. 9A and 9B, a crosslinked bond 21c is created by crosslinking analysis or the like in the polymer model 21 created in the first step ST21. In the example shown in FIG. 9B, a plurality of crosslinks 21c are formed between the four polymer models 21A to 21D constituted by the polymer particles 21a and the bonding chains 21b, and a three-dimensional network by the polymer models 21 is formed in the model creation region A. It is formed.

  Next, in the fourth step ST24, as in the first embodiment described above, an interaction is set between the filler models 11A, 11B, 11C, and 11D and the polymer model 21 to perform numerical analysis.

  As described above, according to the present embodiment, the coagulation retention bonds 12AB, 12AC, 12AD, and 12BC between the filler models 11A, 11B, 11C, and 11D in a state in which the polymer model 21 is previously crosslinked through a crosslinking reaction. , 12BD, and 12CD are created, it becomes possible to perform numerical analysis of the composite material in consideration of the three-dimensional network formed by crosslinking of the polymer model 21. Therefore, the composite material analysis method enables more accurate numerical analysis of the composite material while maintaining the filler aggregation structure.

  In the above embodiment, an example of creating aggregated structure-retaining bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD in the second step ST22 before creating the crosslinked bond 21c by the crosslinking analysis in the third step ST23. explained. Aggregate structure-retaining bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD are not limited in the generation timing as long as the numerical analysis is not performed. The aggregated structure-retaining bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD may be created, for example, after forming the crosslinked bond 21c, and the filler model 11A, 11B, 11C, 11D in the crosslinked bond 21c and the fourth step ST24. And may be created after setting the interaction between the polymer model 21 and the polymer model 21. Among these, from the viewpoint of preventing adverse effects on the production of the aggregated structure-retaining bonds 12AB, 12AC, 12AD, 12BC, 12BD, and 12CD by the crosslinked bond 21c, the aggregated structure-retained bonds 12AB, 12AC, 12AD, It is preferable to create 12BC, 12BD, and 12CD.

  Next, the composite material analysis method and the composite material analysis computer program according to the present embodiment will be described in more detail. FIG. 10 is a functional block diagram of an analysis apparatus that executes the composite material analysis method according to the present embodiment.

  As shown in FIG. 10, the analysis method of the composite material according to the present embodiment is realized by an analysis device 50 that is a computer including a processing unit 52 and a storage unit 54. This analysis device 50 is electrically connected to an input / output device 51 having an input means 53. The input means 53 processes various physical property values of the polymer and filler for which a composite material analysis model is to be created, the actual measurement result of the extension test result using the composite material containing the polymer and filler, and the boundary conditions in the analysis. Input to the unit 52 or the storage unit 54. As the input means 53, for example, an input device such as a keyboard and a mouse is used.

  The processing unit 52 includes, for example, a central processing unit (CPU) and a memory. The processing unit 52 reads a computer program from the storage unit 54 and develops it in a memory when executing various processes. The computer program expanded in the memory executes various processes. For example, the processing unit 52 expands data relating to various processes stored in advance from the storage unit 54 to an area allocated to itself on the memory as necessary, and analyzes the composite material based on the expanded data. Various processes relating to composite material analysis using a model and a composite material analysis model are executed.

  The processing unit 52 includes a model creation unit 52a, a condition setting unit 52b, and an analysis unit 52c. The model creation unit 52a is based on data stored in the storage unit 54 in advance, and the number of particles, the number of molecules, and the molecular weight of the composite material such as filler and polymer when creating the composite material analysis model 1 by the molecular dynamics method. , Molecular chain length, number of molecular chains, branching, shape, size, reaction time, reaction conditions, arrangement of components such as the number of molecules included in the model for analysis to be created, setting and number of calculation steps, etc. Set the coarse-grained model. In addition, the model creation unit 52a sets initial conditions for various calculation parameters such as interactions between the filler particles 11a, between the polymer particles 21a, and between the filler and the polymer particles such as hydrogen bonds and intermolecular forces. In addition, the model creation unit 52a may create a cross-linking analysis such as creation of a cross-linked bond 21c by cross-linking of the polymer model 21 as necessary.

  As calculation parameters for adjusting the interaction between the filler particles 11a and the interaction between the polymer particles 21a, σ and ε of Leonard-Jones potential expressed by the following formula (1) are used, and these are adjusted. By increasing the upper limit distance (cutoff distance) for calculating the potential, it is possible to adjust the attractive force and repulsive force that worked to a long distance. It is preferable that the interaction parameter between the filler particles 11a and the interaction between the polymer particles 21a are sequentially reduced until the interaction between the filler particles 11a and the interaction between the polymer particles 21a reach a constant value. By gradually bringing the σ and ε of the Leonard-Jones potential closer to the original values from large values, it is possible to approach the particles at a gentle speed that does not lead the molecule to an unnatural state. Further, by gradually reducing the cut-off distance, the attractive force and the repulsive force can be adjusted within an appropriate range.

  The condition setting unit 52b sets various analysis conditions such as numerical analysis such as temperature change analysis and transformation analysis, deformation analysis such as extension analysis and shear analysis, and motion analysis such as relaxation analysis.

  The analysis unit 52c performs various numerical analyzes of the composite material analysis model 1 based on the analysis conditions set by the condition setting unit 52b. The analysis unit 52c creates at least one aggregated structure holding bond between the plurality of filler models created by the model creation unit 52a. Here, the analysis unit 52c creates an agglomeration structure-holding bond between the surfaces of the filler model and between the center portions. In addition, the analysis unit 52c sets the extended length of the bond length and the like for the aggregated structure holding bond. Further, the analysis unit 52c sets the equilibrium length of the aggregated structure holding bond. The analysis unit 52c acquires a physical quantity by performing a numerical analysis by a molecular dynamics method using the composite material analysis model 1 created by the model creation unit 52a. Here, the analysis unit 52c executes deformation analysis and relaxation analysis such as extension analysis and shear analysis as numerical analysis. Further, the analysis unit 52c acquires a value such as a displacement obtained as a result of the motion analysis or a physical quantity such as a strain obtained by performing a predetermined calculation process on the obtained value.

  The storage unit 54 is a non-volatile memory that is a readable recording medium such as a hard disk device, a magneto-optical disk device, a flash memory, and a CD-ROM, and a read / write operation such as a RAM (Random Access Memory). A volatile memory which is a possible recording medium is appropriately combined.

  In the storage unit 54, data on fillers such as rubber carbon black, silica, and alumina, which are data for creating a model for analysis of a composite material to be analyzed via the input means 53, rubber, resin, and elastomer Such as polymer data such as, a stress strain curve which is a preset physical quantity history, a method of creating the composite material analysis model 1 according to the present embodiment, and a computer program for realizing the composite material analysis method are stored. ing. This computer program may be capable of realizing the composite material analysis method according to the present embodiment in combination with a computer program already recorded in a computer or computer system. The “computer system” here includes hardware such as an OS (Operating System) and peripheral devices.

  The display means 55 is a display device such as a liquid crystal display device. The storage unit 54 may be in another device such as a database server. For example, the analysis device 50 may access the processing unit 52 and the storage unit 54 by communication from a terminal device including the input / output device 51.

  Next, with reference to FIG. 1 again, the composite material analysis method according to the present embodiment will be described in more detail.

  First, as shown in FIG. 1, the model creation unit 52a creates a plurality of uncrosslinked polymer models 21 including polymer particles 21a and bonding chains 21b in a predetermined model creation region A, and includes a plurality of filler particles 11a. A composite material analysis model 1 including the filler model 11 is created (first step ST11). As shown in FIG. 2, the uncrosslinked polymer model 21 is formed by connecting a plurality of polymer particles 21a with a bonding chain 21b. Here, the model creation unit 52 a places the uncrosslinked polymer model 21 in the created filler model 11. Next, the model creation unit 52a performs balancing calculation after setting initial conditions. In the equilibration calculation, molecular dynamics calculation is performed at a predetermined temperature, density, and pressure for a predetermined time for various components after the initial setting to reach an equilibrium state. The model creation unit 52a then sets the polymer model 21 and the filler model 11 in the model creation region A for creating the composite material analysis model 1 set in the calculation region after the initial condition setting and equilibration calculation processing. An analysis model 1 for a composite material including Moreover, the model creation part 52a may mix | blend modifiers, such as a hydroxyl group, a carbonyl group, and a functional group of an atomic group which raise affinity with a filler to a polymer as needed. Further, the model creation unit 52a may introduce a cross-linked bond 21c into the created polymer model 21 by cross-linking analysis.

  Next, the condition setting unit 52b sets various conditions for executing cross-linking analysis, numerical analysis, and motion analysis (simulation) by the molecular dynamics method using the composite material analysis model 1 created by the model creation unit 52a. Set. The condition setting unit 52 b sets various conditions based on the input from the input unit 53 and the information stored in the storage unit 54. Various conditions include the position and number of the filler model 11 for performing the analysis, the position and number of the filler atom, the filler atomic group, the filler particle 11a and the filler particle group, the filler particle number, the position and number of the molecular chain of the polymer, the polymer Change the position and number of atoms, polymer atomic groups, polymer particles 21a and polymer particles, polymer particle number, position and number of bonding chain 21b, number of bonding chain 21b, stress strain curve and conditions that are preset physical quantity history Not including fixed values.

  Next, the analysis unit 52c creates at least one aggregated structure holding bond between the plurality of filler models 11 created by the model creation unit 52a (second step ST12). Here, the analysis part 52c is good also as what does not define the extension length of the bond length for the aggregation structure retention bond. Further, the analysis unit 52c may create an agglomeration structure holding bond between the center portions of the filler model 11. Further, the analysis unit 52c may set the equilibrium length of the aggregate structure holding bond to be equal to or greater than the sum of the radii of the pair of filler models 11 provided with the aggregate structure holding bond.

  Next, the analysis unit 52c sets an interaction in the composite material analysis model 1 and performs various numerical analyzes such as a temperature change analysis and a voltage transformation analysis. The analysis unit 52c may, for example, combine the filler particles 11a, the polymer particles 21a, the interaction between the filler particles 11a and the polymer particles 21a, and the filler particles 11a and the polymer particles 21a with a bonding chain 21b. Set the interaction of the selected state. Next, the analysis unit 52c performs various numerical analysis such as relaxation analysis by the molecular dynamics method using the composite material analysis model 1, extension analysis, and deformation analysis such as shear analysis. Further, the analysis unit 52c acquires various physical quantities such as a nominal strain obtained by calculating a motion displacement and a nominal stress or a motion displacement obtained from the calculation result of the numerical analysis. By such numerical analysis and kinematic analysis, the bond length and polymer particle speed of the composite model 1 for analysis of the composite material that changes at every analysis time, the speed or bond length between the crosslinking points and the free ends, the orientation, etc. Relationship between the numerical value representing the state change of the segment such as a physical quantity and strain, the relationship between the numerical value representing the state change of the segment such as the bond length of the polymer molecule changing at each analysis time and the polymer particle velocity and the pressure or analysis time Since it is possible to evaluate the relationship between temperature or analysis time and the numerical value representing the state change of the segment, such as the bond length of the polymer molecule that changes with the analysis time and the velocity of the polymer particle, the details of the local molecular state change Analysis is possible. Next, the analysis unit 52 c stores the analysis result of the analyzed composite material in the storage unit 54.

  Moreover, it is preferable that the analysis part 52c subtracts the stress based on the said aggregation structure holding | maintenance coupling | bonding from the stress distortion curve obtained as a calculation result by numerical analysis. As a result, the analysis method of the composite material can remove the energy necessary for holding the filler aggregate structure by the aggregate structure retention bond during the numerical analysis from the stress-strain curve obtained by the numerical analysis. It is possible to accurately evaluate the influence on the polymer chain.

(Example)
Next, examples performed for clarifying the effects of the present invention will be described. In addition, this invention is not limited at all by the following examples.

  The present inventors create a composite material analysis model including a plurality of polymer models and a plurality of filler models, perform elongation analysis under various analysis conditions using the prepared composite material analysis model, calculate time and The relationship with the elastic modulus was investigated. The inventors of the present invention have a general analysis condition in the case where an elongation analysis is performed under an analysis condition for creating an aggregated structure holding bond between the centers of the filler models (Example 1) and the composite model for analysis of the created composite material. When elongation analysis is performed under analysis conditions in which repulsive force acts between each filler model (Comparative Example 1), and when elongation analysis is performed under analysis conditions in which an interaction potential having a large attractive force range is set between multiple filler models (comparison) In Example 2), the relationship between the aggregation state, calculation time, and elastic modulus of the filler model was examined. The contents examined by the inventors will be described below.

  FIG. 11 is a conceptual diagram of a composite material analysis model according to Example 1 and Comparative Examples 1 and 2. As shown in FIG. 11, the analysis model of the composite material used in Example 1 and Comparative Examples 1 and 2 includes four filler models 11A, along one side of a rectangular model creation region A in plan view. 11B, 11C, and 11D had a filler aggregate structure.

  12A is a conceptual diagram of a model for analyzing a composite material after elongation analysis according to Example 1. FIG. As shown in FIG. 12, in Example 1, the four filler models 11A, 11B, 11C, and 11D have moved slightly compared to before the extension analysis, but within the model creation region A even after the extension analysis. Four filler models 11A, 11B, 11C, and 11D retained a filler aggregate structure.

  FIG. 12B is a conceptual diagram of a composite analysis model after elongation analysis according to Comparative Example 1 of the present invention. As shown in FIG. 12B, in the comparative example 1, the four filler models 11A, 11B, 11C, and 11D are moved greatly apart from each other as compared with before the extension analysis, and the four filler models 11A, 11B, and 11C are separated from each other. 11D filler aggregation structure was eliminated.

  FIG. 12C is a conceptual diagram of a composite analysis model after elongation analysis according to Comparative Example 2 of the present invention. As shown in FIG. 12C, in Comparative Example 2, the four filler models 11A, 11B, 11C, and 11D are moved as compared with those before the extension analysis. One filler model 11A, 11B, 11C, 11D retained the filler aggregated structure.

  FIG. 13 is a diagram showing a stress strain curve of an analysis model of a composite material according to an example of the present invention. As shown in FIG. 13, when the stress strain curves of Example 1, Comparative Example 1 and Comparative Example 2 are compared, the increase in strain accompanying the increase in stress is shown in Example 1 (see solid line L1) and Comparative Example 1 (one point). It turns out that it becomes small in order of the comparative example 2 (dotted line L3). As a result, in Example 1, since the filler aggregate structures of the four filler models 11A, 11B, 11C, and 11D were maintained before and after the elongation analysis, the filler aggregate structure strongly influences the increase in stress, resulting in distortion. This is thought to be due to the increase. In Comparative Example 1, since the filler aggregate structures of the four filler models 11A, 11B, 11C, and 11D have been eliminated after the elongation analysis, the filler aggregate structure has no influence on the increase in stress and the distortion is small. It is thought that it became. Further, in Comparative Example 2, the filler aggregate structures of the four filler models 11A, 11B, 11C, and 11D were retained before and after the elongation analysis, but the filler aggregate structure was slightly dispersed as compared with Example 1. It is considered that the increase in strain with respect to the increase in stress was worse than that in Example 1.

  As shown in Table 1, in Example 1, the calculation time is the same as in Comparative Example 1 in which no aggregated structure-retaining bond is provided, but it can be seen that the elastic modulus is greatly increased. Further, in Comparative Example 2, the elastic modulus obtained the same result as in Example 1, but an analysis in which attractive force acts on most of the plurality of filler models 11A, 11B, 11C, and 11D. Since the extension analysis was performed under the conditions, it can be seen that the calculation time significantly increased with respect to Example 1.

  As described above, according to the above-described first embodiment, not only can an extension analysis be performed in which filler aggregate structures of a plurality of filler models 11A, 11B, 11C, and 11D are held before and after the extension analysis, but also a significant increase in calculation time is prevented. On the other hand, it can be seen that the analysis result of the elongation analysis of the composite material reflecting the state in which the filler aggregation structure is retained is obtained.

DESCRIPTION OF SYMBOLS 1 Model for analysis of composite material 11A, 11B, 11C, 11D Filler model 11a Filler particle 12AB, 12AC, 12AD, 12BC, 12BD, 12CD Aggregate structure retention bond 21, 21A, 21B, 21C, 21D Polymer model 21a Polymer particle 21b Bond Chain 21c Cross-linking 50 Analysis device 51 Input / output device 52 Processing unit 52a Model creation unit 52b Condition setting unit 52c Analysis unit 53 Input unit 54 Storage unit 55 Display unit A Model creation region

Claims (7)

A composite material analysis method using a composite material analysis model created by a molecular dynamics method using a computer,
A first step of creating a model for analyzing the composite material including a polymer model modeling a polymer and a plurality of filler models modeling a filler;
A second step of creating at least one aggregated structure retention bond between the plurality of filler models;
And a third step of performing a numerical analysis of the analysis model of the composite material in which the aggregated structure-retaining bond is created.   The method for analyzing a composite material according to claim 1, further comprising a step of crosslinking the polymer model.   The method for analyzing a composite material according to claim 1, wherein the aggregated structure-retaining bond is one in which an extension length of a bond length is not defined.   The method for analyzing a composite material according to any one of claims 1 to 3, wherein the aggregated structure-retaining bond is created between center portions of the filler model.   The method for analyzing a composite material according to claim 4, wherein an equilibrium length of the aggregated structure-retaining bond is equal to or greater than a sum of radii of a pair of filler models provided with the aggregated structure-retaining bond.   The method for analyzing a composite material according to any one of claims 1 to 5, wherein a stress based on the aggregated structure holding bond is subtracted from a stress strain curve obtained as a calculation result by the numerical analysis.   A computer program for analyzing a composite material, which causes a computer to execute the method for analyzing a composite material according to any one of claims 1 to 6.

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